I thought I should add a follow-up here, in case anyone Googling "FTTP Folkestone" ends up on this thread.
Fibre is now available to me -- but only FTTC. The
fibre checker still says lines to my cabinet (Folkestone (NDFOL) Cabinet P71) will be FTTP only. But when I called BT, they said that my line is FTTC.
I also checked with my current ISP, Sky, (who only offer fibre on FTTC lines) and they say they can now offer a fibre service to me. So I guess Openreach must have changed their minds on FTTP in my area, or the fibre checker database has always been in error.